A Secure Control Learning Framework for Cyber-Physical Systems under Sensor and Actuator Attacks

In this article, we develop a learning-based secure control framework for cyber-physical systems in the presence of sensor and actuator attacks. Specifically, we use a bank of observer-based estimators to detect the attacks while introducing a threat-detection level function. Under nominal conditions, the system operates with a nominal-feedback controller with the developed attack monitoring process checking the reliance of the measurements. If there exists an attacker injecting attack signals to a subset of the sensors and/or actuators, then the attack mitigation process is triggered and a two-player, zero-sum differential game is formulated with the defender being the minimizer and the attacker being the maximizer. Next, we solve the underlying joint state estimation and attack mitigation problem and learn the secure control policy using a reinforcement-learning-based algorithm. Finally, two illustrative numerical examples are provided to show the efficacy of the proposed framework.